Details

Time bar (total: 56.6s)

sample159.0ms

Algorithm
intervals
Results
52.0ms130×body160valid
42.0ms222×body80nan
35.0ms126×body80valid

simplify400.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
400.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

localize26.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.5b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.2b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.2b
(* (/ t l) (/ t l))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
21×sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
6×div-inv
5×cbrt-undiv div-exp associate-/l*
4×prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square flip3-+ flip-+ associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 sqrt-div div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 152
Calls
4 calls:
Slowest
31.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
24.0ms
(* (/ t l) (/ t l))
7.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
129.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
45.0ms
(* (/ t l) (/ t l))
21.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify15.4s

Counts
156 → 164
Calls
156 calls:
Slowest
401.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
379.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
315.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
311.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
301.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))

prune2.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.5b

localize59.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.5b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.2b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
80×times-frac
61×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×insert-posit16 add-log-exp
3×sqrt-prod
2×pow2 frac-times pow-plus sqrt-div pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×rem-sqrt-square asin-acos sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 161
Calls
4 calls:
Slowest
31.0ms
(* (/ t l) (/ t l))
22.0ms
(* (/ Om Omc) (/ Om Omc))
7.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series171.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
41.0ms
(* (/ Om Omc) (/ Om Omc))
33.0ms
(* (/ t l) (/ t l))
13.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify7.7s

Counts
169 → 173
Calls
169 calls:
Slowest
526.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
432.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
424.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
280.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
267.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))

prune2.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.8b

localize59.0ms

Local error

Found 4 expressions with local error:

14.8b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
14.8b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
14.8b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
8.7b
(sqrt (* (/ 1 (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
6×cbrt-div
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×flip3-+ pow1/3 sqrt-div flip-+
2×sqrt-pow1
1×frac-times pow1/2 pow-prod-down associate-*l/ associate-*r/ sqrt-prod
Counts
4 → 57
Calls
4 calls:
Slowest
90.0ms
(sqrt (* (/ 1 (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
11.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
4.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
4.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series922.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
381.0ms
(sqrt (* (/ 1 (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
192.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
175.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
174.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify4.9s

Counts
33 → 69
Calls
33 calls:
Slowest
476.0ms
(cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
417.0ms
(cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
388.0ms
(cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
288.0ms
(sqrt (* 1 (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
270.0ms
(* (/ 1 (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

prune1.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.8b

localize36.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
8.7b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
8.0b
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
8.0b
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
48×sqrt-prod
38×add-sqr-sqrt
32×times-frac
30×*-un-lft-identity
24×add-cube-cbrt
12×difference-of-squares
8×pow1
6×rem-sqrt-square
4×sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log associate-/r/ insert-posit16 add-log-exp
2×flip3-+ sqrt-div flip-+ div-inv
Counts
4 → 96
Calls
4 calls:
Slowest
17.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
12.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
1.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
1.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

series374.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
155.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
31.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
28.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

simplify11.7s

Counts
72 → 108
Calls
72 calls:
Slowest
327.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
320.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
307.0ms
(sqrt (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1)))))
296.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
295.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))

prune2.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.8b

regimes690.0ms

Accuracy

98.2% (0.1b remaining)

Error of 5.4b against oracle of 5.4b and baseline of 10.3b

bsearch13.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.8s3923×body160valid
1.6s7688×body80nan
1.3s4077×body80valid